Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant.

F = G m1*m2/r^2

Use Newton's Law of Gravitation to compute the work W required to propel a 800 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98 x 10^24 kg and is concentrated at its center. Take the radius of the earth to be 6.37 x 10^6 m and G = 6.67 x 10^-11 Nm^2/kg^2. (Round your answer to three significant digits.)

Question

Physics

Tommy Hess

21 August, 05:59

Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant.

F = G m1*m2/r^2

Use Newton's Law of Gravitation to compute the work W required to propel a 800 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98 x 10^24 kg and is concentrated at its center. Take the radius of the earth to be 6.37 x 10^6 m and G = 6.67 x 10^-11 Nm^2/kg^2. (Round your answer to three significant digits.)

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Answers (1)

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Tammy · Answer 1

W = - 5.01 10¹⁰ J

Explanation:

Work is defined by the expression

W = ∫ F. dr

Where the blacks indicate vectors, in the case the force is radial and the distance is also radial, whereby the scalar producer is reduced to an ordinary product

W = ∫ F dr

W = G m₁m₂ ∫ 1 / r² dr

W = G m₁ m₂2 (-1 / r)

We evaluate between the lower limits r = Re and upper r = ∞

W = G m₁m₂ (-1 / Re + 1 / ∞)

W = - G m₁ m₂ / Re

Let's calculate

W = - 6.67 10⁻¹¹ 800 5.98 10²⁴ / 6.37 10⁶

W = - 5.01 10¹⁰ J